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Data-Driven Method to Estimate Nonlinear Chemical Equivalence.

Mayo M, Collier ZA, Winton C, Chappell MA - PLoS ONE (2015)

Bottom Line: There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest.However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors.The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements.

View Article: PubMed Central - PubMed

Affiliation: Environmental Laboratory, US Army Engineer Research and Development Center, Vicksburg, MS, 39183, United States of America.

ABSTRACT
There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest. Methods currently employed in fields such as life-cycle assessment, risk assessment, mixtures toxicology, and pharmacology rely mostly on heuristic arguments to justify the use of linear relationships in the construction of "equivalency factors," which aim to model these concentration-concentration correlations. However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors. We address this problem by reporting a method to determine a concentration-concentration relationship between two chemicals based on the full extent of experimentally derived concentration-response curves. Although this method can be easily generalized, we develop and illustrate it from the perspective of toxicology, in which we provide equations relating the sigmoid and non-monotone, or "biphasic," responses typical of the field. The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements. We demonstrate the method using real-world examples of toxicological data which may exhibit sigmoid and biphasic mortality curves. Finally, we use our models to calculate equivalency factors, and show that traditional results are recovered only when the concentration-response curves are "parallel," which has been noted before, but we make formal here by providing mathematical conditions on the validity of this approach.

No MeSH data available.


Related in: MedlinePlus

Non-monotone, or “biphasic,” response function.Positive (red line) and negative (blue line) affectors combine to result in a biphasic response function.
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pone.0130494.g002: Non-monotone, or “biphasic,” response function.Positive (red line) and negative (blue line) affectors combine to result in a biphasic response function.

Mentions: Beckon et al. [23] assumed that such positive and negative affectors contributed separately to the overall concentration-response curve, but relied on the value of a threshold concentration for affector “sensitivity.” If these positive and negative effects coordinate independently, and if the sensitivity thresholds can be taken as sigmoid-type equations of the dose/exposure concentration—as justified in [23] by heuristic arguments, then Beckon et al. argued that a concentration-response for the novel chemical may be expressed by the equation:Ex: f(Cnovel)=[1+(Cnovel/Knovel−)m−][Umax+Uf(Cnovel/Knovel+)m+]−Umax+Ui[1+(Cnovel/Knovel−)m−][1+(Cnovel/Knovel+)m+](4)We have written this equation in terms of approximate “lower” (-) and “upper” (+) sigmoid-like components of the biphasic response, illustrated in Fig 2, which can be delineated by a concentration: (Eq 7 below, and S1 File). Conceptually this may correspond to regimes wherein, e.g., a toxic response differs mechanistically between lower concentrations () and higher concentrations (). If these mechanisms exist and are mostly independent of one another, then each “half” of the biphasic relationship can be modeled approximately as a sigmoid response, and is representative of cumulative exposure effects.


Data-Driven Method to Estimate Nonlinear Chemical Equivalence.

Mayo M, Collier ZA, Winton C, Chappell MA - PLoS ONE (2015)

Non-monotone, or “biphasic,” response function.Positive (red line) and negative (blue line) affectors combine to result in a biphasic response function.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4497723&req=5

pone.0130494.g002: Non-monotone, or “biphasic,” response function.Positive (red line) and negative (blue line) affectors combine to result in a biphasic response function.
Mentions: Beckon et al. [23] assumed that such positive and negative affectors contributed separately to the overall concentration-response curve, but relied on the value of a threshold concentration for affector “sensitivity.” If these positive and negative effects coordinate independently, and if the sensitivity thresholds can be taken as sigmoid-type equations of the dose/exposure concentration—as justified in [23] by heuristic arguments, then Beckon et al. argued that a concentration-response for the novel chemical may be expressed by the equation:Ex: f(Cnovel)=[1+(Cnovel/Knovel−)m−][Umax+Uf(Cnovel/Knovel+)m+]−Umax+Ui[1+(Cnovel/Knovel−)m−][1+(Cnovel/Knovel+)m+](4)We have written this equation in terms of approximate “lower” (-) and “upper” (+) sigmoid-like components of the biphasic response, illustrated in Fig 2, which can be delineated by a concentration: (Eq 7 below, and S1 File). Conceptually this may correspond to regimes wherein, e.g., a toxic response differs mechanistically between lower concentrations () and higher concentrations (). If these mechanisms exist and are mostly independent of one another, then each “half” of the biphasic relationship can be modeled approximately as a sigmoid response, and is representative of cumulative exposure effects.

Bottom Line: There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest.However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors.The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements.

View Article: PubMed Central - PubMed

Affiliation: Environmental Laboratory, US Army Engineer Research and Development Center, Vicksburg, MS, 39183, United States of America.

ABSTRACT
There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest. Methods currently employed in fields such as life-cycle assessment, risk assessment, mixtures toxicology, and pharmacology rely mostly on heuristic arguments to justify the use of linear relationships in the construction of "equivalency factors," which aim to model these concentration-concentration correlations. However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors. We address this problem by reporting a method to determine a concentration-concentration relationship between two chemicals based on the full extent of experimentally derived concentration-response curves. Although this method can be easily generalized, we develop and illustrate it from the perspective of toxicology, in which we provide equations relating the sigmoid and non-monotone, or "biphasic," responses typical of the field. The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements. We demonstrate the method using real-world examples of toxicological data which may exhibit sigmoid and biphasic mortality curves. Finally, we use our models to calculate equivalency factors, and show that traditional results are recovered only when the concentration-response curves are "parallel," which has been noted before, but we make formal here by providing mathematical conditions on the validity of this approach.

No MeSH data available.


Related in: MedlinePlus